From the town of Silverton, drive east to the edge of town and one block past the courthouse, where the paved road splits, go straight. Then, drive north on Road 110, (or 10 according to some sources), a graded dirt road, all the way to the old townsite of Gladstone. Note that another fork of this road 110 goes up along the Animas River from out of Silverton if using the Trails Illustrated map #141. The road along the Animas is signed with a blue sign that reads County Road 2. Do not take that fork. At the intersection around Gladstone, head SE a brief distance, follow a switchback up a little then turn south on road 52 that climbs into the upper South Fork of Cement Creek where it terminates just below a small, unnamed lake. Park here. The last two miles on road 52 will be rougher. A higher clearance vehicle is recommended.
You can car-camp overnight at or around the trailhead or at a few other possible spots on the last two miles in above Gladstone. Be careful regarding private property.
From the trailhead, follow a faint old trail eastward as it takes you up to an old mine at 12,110 ft. Leave the trail at the mine and continue NE or east to the ridge high above the valley floor. Most of this part of the ascent will be on tundra. Once on the ridge, turn south and follow the ridgeline on a steepening gradient to the 12,931 point. You should see a trail coming in from the drainage to the SE. Follow that trail directly south as it heads along the ridge to the next marked highpoint at 13,060 ft. Depart the trail and continue following the main ridge SE toward Tower Mtn. Even though much of this ridge walk appears very narrow on the map, it is never problematic. gain the final 500 feet to the summit of Tower. Most of the ridge hike will be on tundra with some talus and moderately rocky sections. From the dominant summit, take in the surrounding views of the verdant green valleys below. The tundra here in mid-summer looks like a green carpet that's been rolled out across the mountains.
From Tower, you may want to consider a trip over to Dome (feasible) or on your way back down, turn off to the west and bag UN13,325. Climbing Storm Peak from this access would be much more difficult than the route we took.